Abstract
It is well known that perturbation theory in quantum mechanics and quantum field theory generates a divergent series. It has been shown recently (hep-th/9609139) that such divergence can be understood in the context of Lebesgue’s dominated convergence theorem. That theorem governs the validity of the formal manipulation done to generate the perturbative series in the functional integral formalism. It was shown that one of its hypothesis is violated in theories like the λø4 theory in 1, 2 or 3 space-time dimensions. Question: given that in 4 dimensions a new source of divergence appears (renormalons), can they also be understood in the context of Lebesgue’s theorem?
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© 1997 Springer Science+Business Media New York
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Pernice, S.A. (1997). On the Mechanism Underlying the Divergence of Perturbation Theory. In: DeWitt-Morette, C., Cartier, P., Folacci, A. (eds) Functional Integration. NATO ASI Series, vol 361. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0319-8_28
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DOI: https://doi.org/10.1007/978-1-4899-0319-8_28
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